/**
* Copyright (C) 2009 - present by OpenGamma Inc. and the OpenGamma group of companies
*
* Please see distribution for license.
*/
package com.opengamma.analytics.financial.model.volatility.surface;
import static org.testng.AssertJUnit.assertEquals;
import org.testng.annotations.Test;
import org.threeten.bp.ZonedDateTime;
import com.opengamma.analytics.financial.model.interestrate.curve.YieldCurve;
import com.opengamma.analytics.financial.model.option.definition.EuropeanVanillaOptionDefinition;
import com.opengamma.analytics.financial.model.option.definition.OptionDefinition;
import com.opengamma.analytics.financial.model.option.definition.SABRDataBundle;
import com.opengamma.analytics.math.curve.ConstantDoublesCurve;
import com.opengamma.analytics.math.function.RealPolynomialFunction1D;
import com.opengamma.analytics.math.rootfinding.CubicRealRootFinder;
import com.opengamma.analytics.math.rootfinding.QuadraticRealRootFinder;
import com.opengamma.analytics.math.surface.ConstantDoublesSurface;
import com.opengamma.util.time.DateUtils;
import com.opengamma.util.time.Expiry;
/**
*
*/
public class SABRATMVolatilityCalibrationFunctionTest {
private static final double BETA = 1;
private static final double RHO = 0.3;
private static final double ATM_SIGMA = 0.42;
private static final double KSI = 0.5;
private static final double T = 0.5;
private static final double F = 100;
private static final ZonedDateTime DATE = DateUtils.getUTCDate(2010, 8, 1);
private static final SABRDataBundle DATA = new SABRDataBundle(YieldCurve.from(ConstantDoublesCurve.from(0.0)), 0., new VolatilitySurface(ConstantDoublesSurface.from(ATM_SIGMA)), F, DATE, 0, BETA,
RHO, KSI);
private static final SABRATMVolatilityCalibrationFunction FUNCTION = new SABRATMVolatilityCalibrationFunction();
private static final OptionDefinition OPTION = new EuropeanVanillaOptionDefinition(100, new Expiry(DateUtils.getDateOffsetWithYearFraction(DATE, T)), true);
private static final CubicRealRootFinder CUBIC_ROOT_FINDER = new CubicRealRootFinder();
private static final QuadraticRealRootFinder QUADRATIC_ROOT_FINDER = new QuadraticRealRootFinder();
@Test(expectedExceptions = IllegalArgumentException.class)
public void testNullOption() {
FUNCTION.calibrate(null, DATA);
}
@Test(expectedExceptions = IllegalArgumentException.class)
public void testNullData() {
FUNCTION.calibrate(OPTION, null);
}
@Test
public void testZeroVolOfVol() {
final double beta = 0.5;
final SABRDataBundle data = DATA.withVolOfVol(0).withBeta(beta);
final double f1 = Math.pow(F, 1 - beta);
final double a0 = -ATM_SIGMA * f1;
final double a1 = 1;
final double a2 = 0;
final double a3 = (1 - beta) * (1 - beta) * T / 24 / f1 / f1;
final Double[] roots = CUBIC_ROOT_FINDER.getRoots(new RealPolynomialFunction1D(new double[] {a0, a1, a2, a3}));
assertEquals(roots[0], FUNCTION.calibrate(OPTION, data).getAlpha(), 1e-9);
}
@Test
public void testBetaEqualsOne() {
final double a0 = -ATM_SIGMA;
final double a1 = 1 + (2 - 3 * RHO * RHO) * KSI * KSI * T / 24;
final double a2 = RHO * KSI * T / 4;
final Double[] roots = QUADRATIC_ROOT_FINDER.getRoots(new RealPolynomialFunction1D(new double[] {a0, a1, a2}));
assertEquals(FUNCTION.calibrate(OPTION, DATA).getAlpha(), roots[1], 1e-9);
}
}